The temperature dependence of the mechanical parameters of silicon creates challenges in the use of silicon in micro-electromechanical system (MEMS) devices. For example, the elastic modulus of silicon varies by about −88 ppm/K. Thus, the stiffness or flexibility of a silicon MEMS device or component is dependent upon the temperature. The resonant frequency of a resonator or filter is defined by
  f  =            1              2        ⁢        π              ⁢                  k        m            where k is the stiffness and m the mass of the resonator. Accordingly, the resonant frequency will shift with temperature to smaller values. Frequency shifts of up to −45 K/ppm have been observed. To utilize silicon MEMS resonators as frequency reference devices, which can require an overall frequency accuracy of up to 2 ppm, temperature compensation techniques are often used.
Current temperature compensation techniques include active and passive techniques that attempt to compensate for the Tcf. Active techniques in this context refer to techniques which utilize active elements, such as circuitry. One example of an active temperature compensation techniques includes a fractional phase-locked loop (PLL) combined with a temperature sensor and an A/D converter. In another example, temperature compensation can be accomplished by exploiting the bias voltage dependence of the resonant frequency. A third example known in the art involves actively heating the resonator to keep it at a controlled temperature.
Passive techniques using silicon dioxide or other materials have been proposed, wherein the softening of the silicon is counteracted by combining the silicon with some other material that exhibits favourable characteristics. For example, the silicon can be combined with a second material that gets stiffer rather than softer with temperature. One particular example of such a technique includes a monocrystaline silicon resonator surrounded by an oxide layer. Such an approach, however, in which the resonator is surrounded by oxide, leads to a degradation of other important parameters, including the electromechanical coupling, which accounts for the energy being transferred from the electrical to the mechanical domain and back. In an electrostatically actuated resonator, the electromechanical coupling can be expressed as:
  η  =            ɛ      ⁢                          ⁢      A                      d        2            ⁢              u        Bias            where ∈ is the dielectric constant in the electrical active gap, A the coupling area, d the gap distance between the resonator and the driving electrode and UBias the applied bias voltage. As can be seen from the above equation, the electromechanical coupling is dependant upon the square of the gap d. Further, the motional resistance, which is a measure of the impedance of the resonator in series resonance, is dependant upon the square of the electromechanical coupling, η:
  R  =                    k        ⁢                                  ⁢        m                    Q      ⁢                          ⁢              η        2            where Q is the quality factor of the resonator. Considering that a typical electrical gap is in the range of several hundred nanometers and that an oxide film needs a thickness of one to several micrometers, depending upon the resonator geometry, the motional resistance will dramatically increase. This will in turn significantly degrade the performance of the resonator. Additionally, because there is an interface between oxide and silicon, the quality factor of the resonator will further degrade through interfacial losses.